The recent uptick in popularity of such robust formulations is in no small part due to the fact that they are often tractable and enjoy superior statistical guarantees.
[1]} indicate for instance that the probability that the estimated cost of the Wasserstein DRO formulation does not upper bound the actual unknown cost decays as
\(\mathbb {P}^\infty \left(\mathbb {E}_{\mathbb {P}}(\ell (x,\xi ))>\sup _{\mathbb {P}^{\prime } \in \mathcal {P}} \left\lbrace  \mathbb {E}_{\mathbb {P}^{\prime }}(\ell (x,\xi ))\ : \ \mathbb {P}^{\prime } \in \mathcal {U}_T(\hat{\mathbb {P}}_T) \right\rbrace \right)\le C_1 e^{-C_2 T r^{\max (2,\dim \Sigma )}}\) 
